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SdT This has minus T dS minus S dT, but the dT part is zero because we're at constant temperature.
这一项包含负的Tds和，但是dT的部分等于零,因为温度为常数。
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dT That means that dH is also equal to dH/dT, constant pressure dT. All right, so now I've T ot more dH/dT under constant pressure.
也等于偏H偏T恒压乘以，现在我已经得到了在恒压,状态下的偏H偏。
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So you are supposed to know, for example, if x is t^, you're supposed to know dx/dt is nt^.
接下来你就会知道,例如,如果x=t^,那么dx/dt=nt^
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If T is less than T inversion, you have the opposite case, and dT/dp is greater than zero.
如果T比转变温度低,情况就相反，偏T偏p大于零。
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V So this nR over V. And then, using the relation again, T we can just write this as p over T.
恒定温度下的dp/dT等于nR除以，再次利用状态方程，可以把它写成p除以。
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/T We've got Cv integral from T1 to T2, dT over T is equal to minus R from V1 to V2 dV over V.
左边是Cv乘以，从T1到T2对dT积分。
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du/dV So now our du/dV, dp/dT at constant T is just T times dp/dT which is just p over T minus p, it's zero.
现在我们的恒定温度下的，等于T乘以dp/dT，在这里,等于p除以T，最后再减去p，结果是0。
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du/dT And we discover that du/dT at constant V T is equal to du/dT at constant V.
可以发现恒定体积下的,等于恒定体积下的偏u偏。
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SdT So we have dA is minus S dT minus T dS.
我们得到dA等于负TdS减去。
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So we have dH/dT keeping pressure constant, is du/dT keeping pressure constant.
等于偏U偏T，p恒定加上，偏pv偏T，p恒定。
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SdT So dG is dH minus T dS minus S dT.
所以dG等于dH减去TdS再减去。
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So v of t, v is the limit, and we use the symbol dx/dt for velocity.
点的速度等于一个极限,我们用符号dx/dt表示速度
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V So it's minus T dV/dT at constant p, plus V.
负的T乘以恒定压强下dV/dT，再加上。
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T So we know that T dS/dT at constant volume is Cv over T, T and dS/dT at constant pressure is Cp, over T.
在恒定压强下定压比热容Cp乘以dT除以,所以在恒定体积下dS/dT等于Cv除以，在恒定压强下dS/dT等于Cp除以。
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RT/V this expression becomes Cv dT over T is equal to CvdT/T=-RdV/V minus R dV over V.
这样，or，RT，over，V，bar。，So，now，这个等式就,可以化成。
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T It's Cp dT over T at constant pressure.
定容比热容Cv乘以dT除以。
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That's where that term comes from, du/dV dV/dT.
乘以偏V偏T，p恒定，这项的来源。
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du But here you've got pressure constant. du, T this is du, not H here. du/dT is only equal Cv to Cv when the volume is constant, not when the pressure is constant.
这里是压强横笛，du，这是，不是H，偏U偏,只在体积恒定时等于，而不是压强恒定时。
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dT/dp is positive. dT/dp is positive.
偏T偏p是正数，好的这就是。
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JT dT/dp is positive, well that's mu JT.
偏T偏p就是μ
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OK, so for a constant volume process, du we can write du, partial derivative of dT u with respect to T at constant V, dT, dv plus partial derivative of u at constant V, dV.
好，对于一个恒定体积的过程，我们可以写出,等于偏u偏T，V不变，加上偏u偏V，T不变。
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Now, I hope you guys know that much calculus, that when you take a derivative of a function of a function, namely v square over 2 is a function of v, and v itself is a function of t, then the rule for taking the derivative is first take the v derivative of this object, then take the d by dt of t, which is this one.
我希望你们了解更多的微积分知识,当你对复合函数求导时,也就是说v^/2是关于v的函数,而v本身是关于t的函数,求导的法则应该是,第一步是这一部分对v求导,然后v再对t求导,得到这一部分
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